"If you were to talk to our actuarial team, we fell really good about moving into the new market. We think we hit our sweet spot."

The call focused on the company's results in the first quarter of this year. Wellpoint raised its 2014 forecast again on Wednesday, pushing shares closer to their all-time high.

The news came one month after a Wellpoint executive made headlines for predicting strong rate hikes on the exchanges next year.

Executive Vice President Ken Goulet said an unexpected reduction in government payments to insurers would drive the premium increases.

"On a year-over-year basis on our exchanges, and it will vary by carrier, but all of them will probably be in double-digit plus," Goulet said, according to Bloomberg.

CEO Joe Swedish was asked directly on Wednesday about the potential for double-digit rate increases. He did not rule it out, but avoided making specific predictions.

"I would say it's not an easy one to answer because it's going to vary by market and by product," Swedish said.

He went on to describe the various factors that will play into rate increases next year, including an increase in one ObamaCare tax and an expensive new treatment for hepatitis C.

"The pricing will ultimately be reflective of what we are trying to cover," Swedish said. "If we're required to cover more ... the rates will reflect that."

Jill Becher, a spokeswoman for Wellpoint, emailed later that "rates will vary by market." She did not say whether the company still anticipated some double-digit increases.

Insurers are currently working to file their rates for next year with state insurance commissioners. In some states, those officials have power to reject premium increases they believe are too high.

Swedish was one of a group of health insurance executives who met with President Obama and his staff at the White House on April 17. The administration, which also met with health insurance commissioners, is hoping to use its influence to prevent significant rate hikes.

Wellpoint reported Wednesday that it expects 600,000 customers on the exchanges this year. A total of 90 percent have paid their first premium, DeVeydt said.